The practice of ellipsometry is well established as a non-destructive approach to determining characteristics of sample systems and can be practiced in real time. The topic is well described in a great many number of publication, one such publication being a review paper by Collins, titled "Automatic Rotating Element Ellipsometers: Calibration, Operation and Real-Time Applications", Rev. Sci. Instrum, 61(8) (1990).
In general, the practice of ellipsometry typically involves causing a spectroscopic beam of electromagnetic radiation, in a known state of polarization, to interact with a sample system at some angle of incidence with respect to a normal to a surface thereof, in a plane of incidence. (Note, a plane of incidence contains both a normal to a surface of an investigated sample system and the locus of said beam of electromagnetic radiation). Changes in the polarization state of said beam of electromagnetic radiation which occur as a result of said interaction with said sample system are indicative of the structure and composition of said sample system. The practice of ellipsometry determines said changes in polarization state by proposing a mathematical model of the ellipsometer system and the sample system investigated by use thereof. Experimental data is then obtained by application of the ellipsometer system, and a square error reducing mathematical regression, (typically), is then applied to the end that parameters in the mathematical model which characterize the sample system are evaluated so that the obtained experimental data, and values calculated by use of the mathematical model are essentially identical.
A typical goal in ellipsometry is to obtain, for each wavelength in, and angle of incidence of said beam of electromagnetic radiation caused to interact with a sample system, sample system characterizing PSI and DELTA values, (where PSI is related to a change in a ratio of magnitudes of orthogonal components r.sub.p /r.sub.s in said beam of electromagnetic radiation, and wherein DELTA is related to a phase shift entered between said orthogonal components r.sub.p and r.sub.s, caused by interaction with said sample system; EQU PSI=r.sub.p /r.sub.s ; and EQU DELTA=ARCTAN(&lt;r.sub.p -&lt;r.sub.s)).
As alluded to, the practice of ellipsometry requires that a mathematical model be derived and provided for a sample system and for the ellipsometer system being applied. In that light it must be appreciated that an ellipsometer system which is applied ex-situ to investigate a sample system is, generally, sequentially comprised of:
a. a Source of a beam electromagnetic radiation; PA1 b. a Polarizer element; PA1 c. optionally a compensator element; PA1 d. (additional element(s)); PA1 e. a sample system; PA1 f. (additional element(s)); PA1 g. optionally a compensator element; PA1 h. an Analyzer element; and PA1 i. a Detector System. PA1 a. providing spatially separated input and output windows, at least one of said input and output windows demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a sample system positioned between said input and output windows; PA1 b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said input window, interact with said sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; PA1 c. providing a sample system to said means for supporting a sample system, the composition of said sample system being sufficiently well known so that retardance entered thereby to a polarized beam of electromagnetic radiation of a given wavelength, which is caused to interact with said sample system in a plane of incidence thereto, can be accurately modeled mathematically by a parameterized equation which, when parameters therein are properly evaluated, allows calculation of retardance entered thereby between orthogonal components of a beam of electromagnetic radiation caused to interact therewith in a plane of incidence thereto, given wavelength; PA1 d. providing a mathematical model for said ellipsometer system and said input and output windows and said sample system, comprising separate parameterized equations for independently calculating retardance entered between orthogonal components of a beam of electromagentic radiation caused to pass through each of said input and output windows and interact with said sample system in a plane of incidence thereto; such that where parameters in said mathematical model are properly evaluated, retardance entered between orthogonal components of a beam of electromagentic which passes through each of said input and output windows and interacts with said sample system in a plane of incidence thereto can be independently calculated from said parameterzed equations, given wavelength; PA1 e. obtaining a spectroscopic set of ellipsometric data with said parameterizable sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input window, interact with said parameterizable sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; PA1 f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independently calculating retardance entered between orthogonal components in a beam of electromagnetic radiation caused to pass through said input window, interact with said sample system in a plane of incidence thereto, and exit through said output window. PA1 a. providing spatially separated input and output windows, at least one of said input and output windows demonstrating birefringence when a beam of electromagnetic radiation is caused to pass therethrough, there being a means for supporting a sample system positioned between said input and output windows; PA1 b. positioning an ellipsometer system source of electromagnetic radiation and an ellipsometer system detector system such that in use a beam of electromagnetic radiation provided by said source of electromagnetic radiation is caused to pass through said input window, interact with said sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; PA1 c. providing a sample system to said means for supporting a sample system; PA1 d. providing a mathematical model for said ellipsometer system and said input and output windows and said sample system, comprising, for each of said input window and said output window, separate parameterized equations for retardance for at least one orthogonal component in a beam of electromagnetic radiation provided by said source of electromagnetic radiation, which orthogonal component is directed out of a plane of incidence which said electromagnetic beam makes with said sample system in use, and optionally providing separate parameterized equations for retardance for an in-plane orthogonal component of said beam of electromagnetic radiation, such that retardation entered to said out-of-plane orthogonal component, and optionally to said in-plane orthogonal component, of said beam of electromagnetic radiation by each of said input and output windows, can, for each of said input and output windows, be separately calculated by said parameterized equations, given wavelength, where parameters in said parameterized equations are properly evaluated; PA1 e. obtaining a spectroscopic set of ellipsometric data with said sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input window, interact with said sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; PA1 f. by utilizing said mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating sample system DELTA'S in correlation with in-plane orthogonal component retardation entered to said beam of electromagnetic radiation by each of said input and output windows, and parameters in said mathematical model parameterized equations for out-of-plane retardance entered by said input window and said output window to a beam of electromagnetic radiation caused to pass through said input window, interact with said sample system in said plane of incidence thereto, and exit through said output window. PA1 g. providing a parameterized equation for retardation entered by said sample system to the in-plane orthogonal component of a beam of electromagnetic radiation, and as necessary similar parameterized equations for retardation entered by each of said input and output windows to the in-plane orthogonal component of a beam of electromagnetic radiation; and PA1 h. by utilizing said parameterized mathematical model provided in step d. and said spectroscopic set of ellipsometric data obtained in step e., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered in-plane by said sample system and by said input window and said output window such that the correlation between sample system DELTA'S and the retardance entered by said in-plane orthogonal component of a beam of electromagnetic radiation by each of said input and output windows, at given wavelengths in said spectroscopic set of ellipsometric data, is broken. PA1 g. removing the sample system from said means for supporting a sample system positioned between said input and output windows, and positioning in its place an alternative sample system for which a parameterized equation for calculating in-plane retardance entered to a beam of electromagnetic radiation, given wavelength, can be provided; PA1 h. providing a parameterized equation for retardation entered in-plane to an orthogonal component of a beam of electromagnetic radiation by said alternative sample system which is then positioned on said means for supporting a sample system positioned between said input and output windows, and as necessary similar parameterized equations for retardation entered by each of said input and output windows to the in-plane orthogonal component of a beam of electromagnetic radiation; PA1 i. obtaining a spectroscopic set of ellipsometric data with said alternative sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input window, interact with said alternative sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; PA1 j. by utilizing said parameterized mathematical model for said input window and said output window provided in step d. and said parameterized equation for retardation entered by said alternative sample system provided in step h., and said spectroscopic set of ellipsometric data obtained in step i., simultaneously evaluating parameters in said mathematical model parameterized equations for independent calculation of retardance entered to an in-plane orthogonal component of said beam of electromagnetic radiation by said alternative sample system and by said input window and said output window, such that correlation between DELTA'S entered by said alternative sample system and retardance entered by said in-plane orthogonal component of said beam of electromagnetic radiation, by each of said input and output windows, at given wavelengths in said spectroscopic set of ellipsometric data, is broken, said simultaneous evaluation optionally providing new values for parameters in parameterized equations for calculation of retardance entered in said out-of-plane components of said beam of electromagnetic radiation by each of said input window and said output window; PA1 a1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said input window and output window, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output windows, given wavelength; and PA1 a2. causing an unknown sample system to be present on said means for supporting a sample system; PA1 a3. obtaining a spectroscopic set of ellipsometric data with said unknown sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input window, interact with said alternative sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; and PA1 a4. by utilizing said mathematical model for said input window and said output window in which parameter values in mathematical model parameterized equations, for each of said input window and output window have been fixed, simultaneously evaluating PSI'S and uncorrelated DELTA'S parameters for said unknown sample system. PA1 b1. fixing evaluated parameter values in mathematical model parameterized equations, for each of said input window and output window, such that said parameterized equations allow independent determination of retardation entered between orthogonal components of a beam of electromagnetic radiation caused to pass through said input and output windows, given wavelength; and PA1 b2. causing an unknown sample system to be present on said means for supporting a sample system; PA1 b3. obtaining a spectroscopic set of ellipsometric data with said unknown sample system present on the means for supporting a sample system, utilizing a beam of electromagnetic radiation provided by said source of electromagnetic radiation, said beam of electromagnetic radiation being caused to pass through said input window, interact with said alternative sample system in a plane of incidence thereto, and exit through said output window and enter said detector system; and PA1 b4. by utilizing said mathematical model for said input window and said output window in which parameter values in mathematical model parameterized equations, for each of said input window and output window have been fixed, simultaneously evaluating ALPHA'S and BETA'S for said unknown sample system; PA1 b5. applying transfer functions to said simultaneously evaluated ALPHA'S and BETA'S for said unknown sample system to the end that a data set of effective PSI's and DELTA's for a combination of said windows and said sample system is provided; PA1 b6. providing a mathematical model for said combination of said windows and said sample system which separately accounts for the retardation effects of the presence of said windows and said sample system by parameterized equations; and PA1 b7. by utilizing said mathematical model for said combination of said windows and said sample system which separately accounts for the effects of the presence of at least said windows by parameterized equations; and said data set of effective PSI's and DELTA's for a combination of said windows and said sample system, simultaneously evaluating actual PSI's and DELTA's for said unknown sample system per se.
Each of said components b.-i. must be accurately represented by a mathematical model of the ellipsometer system along with a vector which represents a beam of electromagnetic radiation provided from said source of a beam electromagnetic radiation.
Various ellipsometer configurations provide that a Polarizer or Analyzer or Compensator(s) can be rotated during data acquisition, and are describe variously as Rotating Polarizer (RAE), Rotating Analyzer (RAE) and Rotating Compensator (RCE) Ellipsometer Systems.
Where an ellipsometer system is applied to investigate a sample system present in a vacuum chamber, it must be appreciated that the beam of electromagnetic radiation must enter through an input window in said vacuum chamber, and exit via an output window therein. In effect this adds said input and output windows as elements in the ellipsometer system as "additional elements", (eg d. and f. above), which additional elements must be accounted for in the mathematical model. If this is not done, sample system representing parameters determined by application of the ellipsometer system will have the effects of said input and output windows at least partially correlated thereinto, much as if the input and output windows were integrally a part of the sample system.
It is further noted that where two sequentially adjacent elements in an ellipsometer system are held in a static position with respect to one another while experimental ellipsometric data is acquired, said two sequentially adjacent elements generally appear to be a single element.
In-situ application of ellipsometry to investigation of a sample system present in a vacuum chamber then presents a challenge to users of ellipsometer systems in the form of providing a mathematical model for each of said input and output windows, and providing a method by which the effects of said windows can be separated from the effects of an investigated sample system. (It is noted that input and output windows in a vacuum chamber are structurally positioned by said vacuum chamber and are not rotatable with respect to a sample system present in said vacuum chamber in use, thus preventing breaking correlation between parameters in equations for sequentially adjacent input and output windows and an investigated sample system by an element rotation technique). While correlation of parameters in mathematical equations which describe the effects of groupings of elements, (such as a compensator and an optional element(s)), can be tolerable, correlation between parameters in the mathematical model of an investigated sample system and other elements in the ellipsometer system must be broken to allow obtaining accurate sample system representing PSI and DELTA values, emphasis added. That is to say that correlation between parameters in a equations in a mathematical model which describe the effects of a stationary compensator and a sequentially next window element, (eg. correlation between effects of elements c. and d. or between f. and g. identified above), in a beam of electromagnetic radiation might be tolerated to the extent that said correlation does not influence determination of sample system describing PSI and DELTA values, but the correlation between parameters in equations which describe the effects of ellipsometer system components (eg. a., b., c., d., f., g., h. and i.), and equations which describe the effects of a present sample system (eg. element e. above), absolutely must be broken to allow the ellipsometer system to provide accurate PSI and DELTA values for said sample system.
Thus is identified an example of a specific problem, solution of which is the topic of the present invention.
One typical approach to overcoming the identified problem, where space consideration are not critical, and where ellipsometer system configuration can be easily modified, is to obtain multiple data sets with an ellipsometer system configured differently during at least two different data set acquisitions. For instance, a data set can be obtained with a sample system present and in which a beam of electromagnetic radiation is caused to interact with said sample system, and another data set can be obtained with the ellipsometer system configured in a straight-through configuration, where a beam of electromagnetic radiation is caused to pass straight through an ellipsometer system without interacting with a sample system. Simultaneous mathematical regression utilizing both data sets can allow evaluation of sample system characterizing PSI and DELTA values over a range of wavelengths, uncorrelated with present bi-refringent retardation effects of said input and output windows. The problem with this approach is that where ellipsometer systems are fit to vacuum chambers, ellipsometer reconfiguration so as to allow acquisition of such multiple data sets can be extremely difficult, if not impossible to carry out.
Another rather obvious solution to the identified problem is to provide input and output windows which are absolutely transparent at all electromagnetic beam wavelengths utilized. That is, provide input and output windows which do not attenuate the magnitude of r.sub.p or r.sub.s orthogonal components, (or at least do not change their ratio, r.sub.p /r.sub.s), and which also do not enter phase shift between r.sub.p or r.sub.s orthogonal components when said beam of electromagnetic radiation is caused to pass therethrough. While control of the effect of a window on a ratio, (r.sub.p /r.sub.s), of electromagnetic beam orthogonal components can rather successfully, often be accomplished by causing a beam of electromagnetic radiation to approach a surface of a vacuum chamber window along a normal to a surface thereof, this is not the case regarding phase shift entered between r.sub.p and r.sub.s orthogonal components of a said beam of electromagnetic radiation caused to pass therethrough. That is, input and output windows in vacuum chambers typically demonstrate "bi-refringence", in that the r.sub.p orthogonal component is "retarded" by a different amount than is the r.sub.s orthogonal component when said beam of electromagnetic radiation is caused to pass therethrough. To complicate matters, this "bi-refringence" effect also varies with wavelength and with stresses which can develop in a window during use because of temperature and pressure changes etc. This approach is presently utilized with varying degrees of success. For instance, windows provided by BOMCO Inc. --are produced with the goal of eliminating bi-refringence, and are mounted in vacuum chambers using "O" ring seals which help to minimize uneven application of stresses and developed strains thereacross. While some success is achieved via this approach, the BOMCO windows are not "perfect" and do demonstrate some remaining bi-refringence properties, which can an vary in unpredictable ways over a period of usage. In addition, BOMCO windows are expensive, costing on the order of $1000.00 each), and are large in size thereby making adaptation thereof to use in a vacuum chamber difficult at times, particularly in retro-fit scenarios. And, there have been cases where BOMCO windows have broken in use. This is highly undesirable as vacuum chambers are often times caused to contain highly toxic and hazardous materials during, for instance, etching and/or deposition steps required in the fabrication of semiconductor devices.
The alternative to use of the BOMCO windows is to simply use standard vacuum chamber windows, which, while significantly less expensive, demonstrate order of magnitude larger bi-refringence effects. (Note, BOMCO windows provide bi-refringent effects on the order of approximately six-tenths (0.6) to two-tenths (0.2) degrees over a range of wavelengths of from four-hundred (400) to seven-hundred-fifty (750) nanometers, whereas standard vacuum windows demonstrate birefringent effects on the order of six (6.0) to three (3.0) degrees over the same range of wavelengths). (Note, bi-refringent retardation typically follows an approximate inverse wavelength, (eg. 1/wavelength), relationship).
A need is thus identified for a method of practicing ellipsometry which enables the breaking of correlation between parameters in equations which describe retardence entered to orthogonal components of a beam of electromagnetic radiation caused to interact with a sample system, and parameters in equations which describe bi-refringent effects on said orthogonal components in said beam of electromagnetic radiation caused by input and output windows, with a primary, though not limiting, application being in a vacuum chamber setting.
Various researchers have previously noted the identified problem and proposed various first order mathematical model equation correction techniques as solution, which approaches have met with various degrees of success where input and output windows demonstrate on the order of a maximum of two (2) degrees of bi-refringence. This, however, leaves the problem unsolved where bi-refringence approaches six (6.0) degrees, as commonly occurs in standard vacuum windows at wavelengths of four-hundred (400) nanometers and below.
Patents of which the Inventor is aware include U.S. Pat. No. 5,757,494 to Green et al., in which is taught a method for extending the range of Rotating Analyzer/Polarizer ellipsometer systems to allow measurement of DELTAS near zero (0.0) and one-hundred-eighty (180) degrees. Said patent describes the presence of a window-like variable bi-refringent components which is added to a Rotating Analyzer/Polarizer ellipsometer system, and the application thereof during data acquisition, to enable the identified capability.
A patent to Thompson et al. U.S. Pat. No. 5,706,212 teaches a mathematical regression based double fourier series ellipsometer calibration procedure for application, primarily, in calibrating ellipsometers system utilized in infrared wavelength range. Bi-refringent window-like compensators are described as present in the system thereof, and discussion of correlation of retardations entered by sequentially adjacent elements which do not rotate with respect to one another during data acquisition is described therein.
A patent to Woollam et al, U.S. Pat. No. 5,582,646 is disclosed as it describes obtaining ellipsometric data through windows in a vacuum chamber, utilizing other than a Brewster Angle of Incidence.
Patent to Woollam et al, U.S. Pat. No. 5,373,359, patent to Johs et al. U.S. Pat. No. 5,666,210 and patent to Green et al., U.S. Pat. No. 5,521,706, and patent to Johs et al., U.S. Pat. No. 5,504,582 are disclosed for general information as they pertain to Rotating Analyzer ellipsometer systems.
A paper by Johs, titled "Regression Calibration Method for Rotating Element Ellipsometers", Thin Solid Films, 234 (1993) is disclosed as it describes a mathematical regression based approach to calibrating ellipsometer systems.
A paper by Nijs & Silfhout, titled "Systematic and Random Errors in Rotating-Analyzer Ellipsometry", J. Opt. Soc. Am. A., Vol. 5, No. 6, (June 1988), describes a first order mathematical correction factor approach to accounting for window effects in Rotating Analyzer ellipsometers.
A paper by Kleim et al, titled "Systematic Errors in Rotating-Compensator ellipsometry", J. Opt. Soc. Am., Vol 11, No. 9, (September 1994) describes first order corrections for imperfections in windows and compensators in Rotating Compensator ellipsometers.
Principal component analysis and neural network approaches to the problem are discussed in a paper by Pickering et al., titled "Instrumental and Computational Advances for Real-time Processes Control Using Spectroscopic Ellipsometry", Int. Conf. on--Netrology??? and Characterization for VLSI Tech., NIST, (March 1998).
Other papers of interest in the area by Azzam & Bashara include one titled "Unified Analysis of Ellipsometry Errors Due to Imperfect Components Cell-Window Birefringence, and Incorrect Azimuth Angles", J. of the Opt. Soc. Am., Vol 61, No. 5, (May 1971); and one titled "Analysis of Systematic Errors in Rotating-Analyzer Ellipsometers", J. of the Opt. Soc. Am., Vol. 64, No. 11, (November 1974).
Another paper by Straaher et al., titled "The Influence of Cell Window Imperfections on the Calibration and Measured Data of Two Types of Rotating Analyzer Ellipsometers", Surface Sci., North Holland, 96, (1980), describes a graphical method for determining a plane of incidence in the presence of windows with small retardation.
Finally, A paper which is co-authored by the inventor herein is titled "In Situ Multi-Wavelength Ellipsometric Control of Thickness and Composition of Bragg Reflector Structures", by Herzinger, Johs, Reich, Carpenter & Van Hove, Mat. Res. Soc. Symp. Proc., Vol.406, (1996) is also disclosed.
In view of relevant prior art, there remains need for a second order mathematical model equation correction technique which enables breaking correlation between sample system characterization DELTA and in-plane retardence entered to a beam of electromagnetic radiation entered by window(s) through which said beam of electromagnetic radiation is caused to pass. This is particularly true where window bi-refringent retardence exceeds a few degrees, as is the case for standard vacuum chamber windows.